Improved Algorithms for Maximal Clique Search in Uncertain Networks

Enumerating maximal cliques from an uncertain graph is a fundamental problem in uncertain graph analysis. Given an uncertain graph G, a set of nodes C in G is a maximal (k, τ)-clique if (1) |C|>k and C is a clique with probability at least τ, and (2) C is a maximal node set meeting (1). The state-of-the-art algorithm for enumerating all maximal (k, τ)-cliques is very costly when handling large uncertain graphs, as its time complexity is proportional to 2^n where n is the number of nodes in the uncertain graph. To overcome this issue, we propose two new core-based pruning algorithms to reduce the uncertain graph size without missing any maximal (k, τ)-clique. We also develop a novel cut-based optimization technique to further improve the pruning performance of the core-based pruning algorithms. Based on these pruning techniques, we propose an improved algorithm to enumerate all maximal (k, τ)-cliques, and a new algorithm with several novel upper-bounding techniques to compute one of maximum (k, τ)-cliques from the pruned uncertain graph. The results of extensive experiments on six real-world datasets demonstrate the efficiency and effectiveness of the proposed algorithms.